Design Principles Underlying Robust Perfect Adaptation of Complex Biochemical Networks

Biochemical networks are often characterised by tremendous complexity - both in terms of the sheer number of interacting molecules ("nodes") and in terms of the varied and incompletely understood interactions among these molecules ("interconnections" or "edges"). Strikingly, the vast and intricate networks of interacting proteins that exist within each living cell have the capacity to perform remarkably robustly, and reproducibly, despite significant variations in concentrations of the interacting components from one cell to the next, and despite mutability over time of biochemical parameters. Here we consider the ubiquitously observed and fundamentally important signalling response known as Robust Perfect Adaptation (RPA). We have recently shown that all RPA-capable networks, even the most complex ones, must satisfy an extremely rigid set of design principles, and are modular, being decomposable into just two types of network building-blocks - Opposer modules, and Balancer modules. Here we present an overview of the design principles that characterize all RPA-capable network topologies through a detailed examination of a collection of simple examples. We also introduce a diagrammatic method for studying the potential of a network to exhibit RPA, which may be applied without a detailed knowledge of the complex mathematical principles governing RPA.